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If n is an integer then show that (1 ...

If n is an integer then show that
`(1 + cos theta + i sin theta)^(n) + (1 + cos theta - i sin theta )^(n) = 2^(n+1) cos ^(n) ( theta//2) cos ((n theta)/2)`.

Answer

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Knowledge Check

  • (cos theta + sin theta )^(2) + (cos theta - sin theta )^(2) =

    A
    0
    B
    1
    C
    2
    D
    `sqrt(2)`

  • The value of (cos2 theta + i sin 2 theta)^5(sin theta+i cos theta)^4 is

    A
    `cos10 theta+i sin 10 theta`
    B
    `cos6 theta-i sin6theta`
    C
    `cos6 theta+i sin6 theta`
    D
    `cos 10 theta-i sin 10 theta`

  • (cos theta + sin theta )/( cos theta - sin theta )-(cos theta - sin theta )/( cos theta + sin theta ) =

    A
    `2 sin theta `
    B
    `2 cos theta `
    C
    `2 tan 2 theta `
    D
    `2 cot 2 theta `

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    Show that (1 + sin theta)/ cos theta + cos theta / (1 + sin theta) = 2 sec theta

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    If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1- cos theta + sin theta )/(1+ sin theta )

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